Finite Group Databasebeta

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C3×C5×C7×C11×D7 #30633592

order16170
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×C11×D7

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derivedC7 ⋊ C2×C3×C5×C7×C11
HallC5×C72×C11 ⋊ C2×C3
HallC3×C72×C11 ⋊ C2×C5
HallC3×C5×C72 ⋊ C2×C11
HallC72×C11 ⋊ C2×C3×C5
HallC5×C72 ⋊ C2×C3×C11
HallC3×C72 ⋊ C2×C5×C11
SylowC72 ⋊ C2×C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7×C11D7
commutator, cosocle, hypocenterC7C2×C3×C5×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C7
UCSC1 ◁ C3×C5×C7×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

5775 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×D7×D11, C3×C5×C11×D72, C3×C5×D7×D77, …
maximal normal subgroup ofC3×C5×C7×D7×D11, C3×C5×C11×D72, C3×C5×D7×D77, …
maximal quotient ofC3×C5×C7×C11×Dic7, C2×C3×C5×C7×C11×D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 137);